Related papers: A Unified Approach to Attractor Reconstruction
In many geoscientific applications, multiple noisy observations of different origin need to be combined to improve the reconstruction of a common underlying quantity. This naturally leads to multi-parameter models for which adequate…
The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors…
Disentangled distributed representations of data are desirable for machine learning, since they are more expressive and can generalize from fewer examples. However, for complex data, the distributed representations of multiple objects…
Embedding models, which learn latent representations of users and items based on user-item interaction patterns, are a key component of recommendation systems. In many applications, contextual constraints need to be applied to refine…
We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
Time series anomaly detection is an important task, with applications in a broad variety of domains. Many approaches have been proposed in recent years, but often they require that the length of the anomalies be known in advance and…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
Theoretical inverse problems are often studied in an ideal infinite-dimensional setting. The well-posedness theory provides a unique reconstruction of the parameter function, when an infinite amount of data is given. Through the lens of…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
The symplectic geometry mode decomposition (SGMD) is a powerful method for analyzing time sequences. The SGMD is based on the upper conversion via embedding and down conversion via diagonal averaging principle (DAP) inherited from the…
High-dimensional statistical inference deals with models in which the the number of parameters p is comparable to or larger than the sample size n. Since it is usually impossible to obtain consistent procedures unless $p/n\rightarrow0$, a…
An important theme in modern inverse problems is the reconstruction of time-dependent data from only finitely many measurements. To obtain satisfactory reconstruction results in this setting it is essential to strongly exploit temporal…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
When building linear or nonlinear models one is faced with the problem of selecting the best set of variable with which to predict the future dynamics. In nonlinear time series analysis the problem is to select the correct time delays in…
Composed image retrieval aims to find an image that best matches a given multi-modal user query consisting of a reference image and text pair. Existing methods commonly pre-compute image embeddings over the entire corpus and compare these…
In this paper we combine two existing approaches for approximating attractors. One of them approximates the attractors arbitrarily well by sublevel sets related to solutions of infinite dimensional linear programming problems. A downside…
Background: Embedded feature selection in high-dimensional data with very small sample sizes requires optimized hyperparameters for the model building process. For this hyperparameter optimization, nested cross-validation must be applied to…
The celebrated Takens' embedding theorem provides a theoretical foundation for reconstructing the full state of a dynamical system from partial observations. However, the classical theorem assumes that the underlying system is deterministic…
Recurrence networks are a powerful nonlinear tool for time series analysis of complex dynamical systems. {While there are already many successful applications ranging from medicine to paleoclimatology, a solid theoretical foundation of the…